2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60768We show that elements of unital $C^*$-algebras without tracial states are finite sums of commutators. Moreover, the number of commutators involved is bounded, depending only on the given $C^*$-algebra.Functional AnalysisOperator Algebras46L05text